ENGINEER  DEPARTMENT,  U.  S.  ARMY. 


ON  THE  USE  OF  THE  BAROMETER 


ON 


SURVEYS  AND  RECONNAISSANCES. 


A  Compendium,  without  Plates,  of  No.  15 


PROFESSIONAL  PAPERS  OF  THE  CORPS  OF  ENGINEERS. 


LIEUT.  OOL.  E.  S.  WILLIAMSON, 

CORPS  OF  ENGINKERS,  U.  S.  A. 


WASHINGTON: 

GOVERNMENT     PRINTING    OFFICE, 

1878. 


ENGINEER  DEPARTMENT,  U.  S.  ARMY. 


ON  THE  USE  OF  THE  BAROilETER 

ox 

SURVEYS  AND  RECOx\NAISSAXCES, 

IV  BEIXG 

A  Compendium,  without  Plates,  of  No.  15 

OF  THE 

PROFESSIONAL  PAPERS  OF  THE  CORPS  OF  ExNGINEERS. 


LIEUT.  COL.  E.  S.  WILLIAMSON, 

CORPS  OF  ENGINEERS,  U.  S.  A. 


WASHINGTON: 

GOVERNMENT    PRINTING    OFFICE. 

1878. 


■N  b  \ 


i 


Offioe  of  the  Chief  of  Engineers, 

Washington,  D.  C,  August  7,  1878. 
Sir  :  Lieut.  Col.  R,  S.  Williamson,  Corps  of  Engineers, 
has  submitted  to  this  ofBce  a  compendium  (without  plates) 
of  his  paper  "On  the  use  of  the  Barometer,"  &c.,  Professional 
Papers,  Corps  of  Engineers,  Xo.  15. 

This  condensed  work  contains  most  of  the  information  to 
be  found  in  the  larger  one,  with  a  few  tables  which  are  new, 
the  result  of  further  investigation  of  the  subject. 

As  this  compendium  will  be  very  useful  and  convenient 
to  officers  conducting  barometric  reconnaissances,  I  have  the 
honor  to  recommend  that  it  be  printed  at  the  Government 
Printing  Ot3ace,  and  copies  furnished  upon  the  usual  requi- 
sition. 

Very  respectfully,  your  obedient  servant, 

H.  G.  Wright, 
Acting  Chief  of  Engineers. 
Hon.  Geo.  W.  McCrary, 
Secretary  of  War. 

Approved. 

By  order  of  the  Secretary  of  War. 

H.  T.  Crosby, 

Chief  Cleric. 
War  Department, 
August  10,  1878. 


382800 


San  Francisco,  Cal., 

Ajiril  30th,  1878. 
General:  1  have  the  bonor  to  submit  for  your  consid- 
eration a  condensed  copy  of  my  work  on  meteorology  and 
hypsometry,  thinking  that  a  small  volume  of  this  kind  can 
easily  be  carried  in  the  field  and  be  usefully  employed  there, 
while  the  original  work  with  its  plates  is  not  in  a  conven- 
ent  form  for  that  purpose.  This  little  work  contains  most 
of  the  information  to  be  found  in  the  larger  one,  but  1  have 
added  a  few  tables  which  are  new,  the  result  of  further  in- 
vestigation of  the  subject. 

In  the  concluding  remarks  I  have  compared  the  methods 
of  treating  meteorological  observations  with  that  of  Prof.  J. 
D.  Whitney  as  described  in  his  work  entitled  "Contributions 
to  Barometric  Hypsometry,''  and  have  shown  conclusively 
that  there  are  over  forty  per  cent,  more  of  maximum  and 
mean  errors  by  his  method  than  by  mine. 

Very  respectfully,  your  obedient  servant, 

R.  S.  Williamson, 
Lieutenant  Colonel  of  Engineers. 
Brig.  Gen.  A.  A.  Humphreys, 

Chief  of  Engineers,  U.  S.  A. 


TABLE    OF    CONTENTS. 


Page. 
Introduction 11 

Instruments  and  methods  for  determining  altitudes — The  mei- 
curial  and  aneroid  barometers  compared — The  barometric 
formula — The  scales  in  plotting  observations. 

Horary  and  abnormal  oscillation 15 

Their  periods — Horary  corrections — Reduction  to  level — Re- 
duction to  second  level — Rules — Observations — Hourly  and 
at  intervals  compared — Effect  of  season,  altitude,  and  lati- 
tude on  horary  oscillation — Law  of  oscillation. 

Variation  op  temperature 30 

Comparison  of  barometric  and  thermometric  oscillations — 
Elimination  of  effects  of  temperature — Mean  daily  temper- 
ature— Comparisons. 

Hypsometrical  results  from  daily  means 38 

Hypsometrical  results  from  monthly  mkans 43 

Concluding  remarks 45 

Professor  J.  D.  Whitney's  method — Comparison  of  Whitney's 
and  Williamson's  methods. 


i 


LIST    OF    TABLES 


Page. 

Tahle  I. — Showin^j;  the  (liti'.'reiice  between  the  menu  baroiuetric 
pressure  iu  the  ditferent  months  as  obtained  from  the  mean 
of  24  hourly  observations,  and  observations  at  7  a.  m.,  2  p.  m., 
and  9  p.  m.,  the  former  being  assumed  as  the  standard 22 

Taiu,e  II. — Showing  the  diftereuce  between  the  daily  mean  baro- 
metric pressure  as  obtained  from  the  mean  of  24  hourly  obser- 
vations, and  from  corrected  observations  at  7  a.  m.,  2  p.  m., 
9  p.  m.,  and  7  a.  m.  the  next  morning;  and  also  between  the 
first  and  those  obtained  from  observations  at  7  a.  m.,  2  p.  m., 
and  9  p.  m.,  the  first  being  assumed  as  the  standard 25 

Table  III. — Showing  the  difference  between  the  monthly  mean 
barometric  pressure  as  computed  from  observations  at  7  a.  m., 
2  p.  m.,  and  9  p.  m.,  and  6  a.  m.,  noon,  and  6  p.  ra.,  the  former 
being  ijsed  as  a  standard 27 

Taijle  IV. — Showing  the  difference  between  the  niaan  tempera- 
ture in  the  different  months  as  obtained  from  the  mean  of  24 
hourly  observations,  and  those  taken  at  7  a.  m.,  2  p.  m.,  and 
9  p.  m.,  the  former  being  assumed  as  the  standard 35 

Table  V. — Showing  the  difference  between  the  monthly  mean 
temperatures  as  computed  from  observations  at  7  a.  m.,  2  p. 
m.,  and  9  p.  m.,  and  6  a.  m.,  noon,  and  6  p.  m.,  the  former  be- 
ing used  as  a  standard 37 

Table  VI. — Consolidated  table  of  maximum  errors  in  computing 
differences  of  altitude  from  daily  barometric  and  thermo- 
metr ic  means 41 

Table  VII. — Consolidated  table  of  mean  errors  in  computing  dif- 
ferences of  altitude  from  daily  barometric  aud  thermometric        42 
means 

Table  VIII. — Comparison  of  barometric  results  by  Professor  Whit- 
ney's and  Colonel  Williamson's  methods,  from  observations 
taken  at  7  a.  m.,  2  p.  m.,  and  9  p.  m.,  during  W  days  of  Au- 
onst,  1860 49 


INTRODUCTION, 


To  the  large  number  of  engineers,  surveyors,  and  others, 
who  are  and  will  be  engaged  in  developing  the  geography 
of  this  country,  so  large  a  portion  of  which  is  almost  un- 
known or  but  partially  explored,  the  best  method  of  treating 
observations  of  the  barometer  and  thermometer,  so  as  to 
obtain  the  most  reliable  results  in  determining  diiferences 
of  altitude,  is  a  matter  of  the  first  importance.  It  is  well 
known  that  the  mercurial  cistern  barometer  is  the  best  in- 
strument for  that  purpose,  for  the  reason  that  the  spirit- 
level  is  out  of  the  question,  except  within  very  limited  areas, 
the  length  of  time  and  amount  of  labor  required  for  its 
proper  use  being  far  greater  than  can  be  devoted  to  the 
determination  of  the  vertical  element  on  an  ordinary  sur- 
vey. The  only  instrument,  that  can  be  mentioned  as  at  all 
to  be  compared  with  the  cistern-barometer  is  the  handy 
aneroid,  the  defects  of  which,  however,  as  compared  with 
the  mercurial  instrument,  are  so  great  as  to  preclude  its 
being  used  as  a  substitute  for  the  latter.  Besides  the  fact 
that  the  aneroid  is  not  susceptible  of  reading  closer  than 
one  hundredth  of  an  inch,  while  the  mercurial  cistern  can  be 
read  to  one-thousandth,  the  great  defect  that  it  is  liable  at 
any  time  to  change  its  zero,  particularly  in  travelling,  with- 
out there  being  any  evidence  to  show  that  a  change  has 
occurred,  makes  the  instrument  entirely  unreliable  on  a 
survey  of  any  extent.  The  mercurial  cistern  barometer  is, 
then,  the  only  instrument  that  can  be  used  with  any  satisfac- 
tion for  hypsometrical  purposes,  and  the  following  few  pages 
will  be  devoted  to  show  the  best  method  of  using  it  with  its 
accompanying  open  air  thermometer. 


12 

I  may  remark,  in  tLe  first  place,  tliat  whenever  tbe  read- 
ings of  tbe  barometer  are  referred  to  in  tbe  following  pages, 
those  of  the  barometer  reduced  to  32°  Fahrenheit  are  meant. 
In  the  barometric  formula  of  Laplace  and  others,  a  term  has 
been  introduced  to  take  into  account  tbe  effect  of  tbe  ex- 
pansion and  contraction  of  tbe  mercurial  column  by  beat, 
in  order  to  reduce  tbe  readings  to  what  they  would  have 
been  had  tbe  temperature  of  the  instrument  been  always  at 
the  freezing  point.  But  it  is  equally  accurate  and  much 
more  couvenient  to  reduce  each  reading  in  the  first  i)lace 
to  the  freezing  point  by  tbe  tables  which  have  been  pre- 
pared for  the  purpose.  By  adopting  this  course,  the  column 
so  reduced,  when  plotted,  shows  the  movements  of  a  natural 
atmosphere,  and  their  peculiarities  can  be  studied  with 
advantage ;  whereas  tbe  readings  of  the  barometer  not  so 
reduced  give  so  irregular  a  curve,  the  movements  being 
masked  by  tbe  ever-varying  temi)erature  of  the  instrument, 
that  it  is  scarcely  possible  to  discover  any  law  guiding  them, 
if  such  a  law  exists. 

1  also  wish  to  point  out  that,  unless  special  mention  is 
made  to  tbe  contrary,  tbe  formula  used  in  tbe  computations 
is  the  one  found  in  Professional  Papers  of  the  Corps  of 
Engineers,  No.  15,  only  omitting  the  special  correction  for 
the  moisture  in  tbe  atmosphere.  It  is  a  translation  of  tbe 
formula  of  Plantamour.  This  formula  differs  from  the  one 
prepared  by  Guyot  for  the  Smithsonian  Institution,  which 
is,  in  fact,  the  formula  of  Lai)lace,  by  a  very  small  change 
in  the  barometric  constant.  Plantamour  adopts  the  num- 
ber 00,384.3,  while  Guyot  gives  60,lo8.G.  This  slight  change 
causes  the  dittereuce  of  altitude  to  be  greater  by  the  former 
formula  than  by  the  latter  by  a  little  less  than  four  feet  for 
each  thousand  feet  of  difference  of  altitude. 

1  shall  freqaenrly  have  occasion  to  refer  to  the  graphic 
representation  of  meteorological  observations,  which  opera- 
tion is  called  plotting.     In  order  to  represent  the  various 


/ 


13 

movemeuts  of  the  atmosphere  graphically,  and  in  such  a 
I  ^  way  that  the  value  of  the  changes  can  be  measured,  it  is 

necessary  to  attach  scales  to  the  drawings.  In  all  cases  to 
which  I  shall  refer,  the  vertical  scale  is  either  a  scale  of 
inches  of  the  barometric  column,  or  of  degrees  of  the  ther- 
mometer. The  horizontal  scale  is  a  scale  of  hours,  or  days, 
or  mouth,  as  the  case  may  be.  But  as  I  do  not  propose  to 
illustrate  this  paper  by  such  drawings,  I  shall  endeavor  to 
give  my  descriptions  in  such  a  way  that  my  reuiarks  will  be 
easilv  understood  without  them. 


OF   THE   HORARY  AND  AUXORMAL   OSCILLATIONS  OF 
THE  BAROMETER, 


A  study  of  barotnetriu  observations,  extended  over  a 
sufficient  period  of  time,  will  reveal  the  existence  of  two  dis- 
tinct oscillations.  These  Ijave  been  called  respectivelj'  the 
horary  and  abnormal  oscillations.  The  horary  oscillation 
lias  a  period  of  24  hours.  Within  this  period  it  presents, 
except  during  barometric  storms,  two  distinct  maxima 
and  two  minima,  easily  recognizable.  The  abnormal  oscil- 
lation, on  the  other  hand,  is  the  result  of  a  steady  progress- 
ive movement  of  variable  period,  but  usually  it  passes  from 
one  maximum  to  one  minimum  in  from  three  to  six  days. 

When  a  series  of  hourly  observations  of  the  barometer, 
taken  during  ten  or  more  days,  is  plotted,  there  appears  dur- 
ing each  day  a  regular  movement,  more  or  less  marked,  and 
indicating  two  maxima  and  two  minima  in  the  twenty-four 
hours.  If  a  table  is  made  by  taking  separately  the  mean  of 
the  observations  at  the  same  hour  of  each  day,  thus  obtain- 
ing twenty-four  mean  readings  when  the  observations  are 
taken  hourly  and  uninterruptedly,  and  this  mean  table  is 
plotted,  the  mean  curve  so  developed  shows  this  double  os- 
cillation very  decidedly.  If  we  were  to  make  a  grand  meau 
by  adding  up  the  twenty-four  mean  hourly  results,  and 
dividing  by  twenty-four,  and  if  we  then  subtract  each  mean 
result  from  the  grand  meau,  we  have  a  table  in  which  some 
of  the  numbers  would  be  greater  and  some  less  than  the 
grand  mean,  and  therefore  some  would  be  affected  with  a 


16 

plus  and  some  with  a  minus  sign.  This  table  can  be  used 
as  a  table  of  corrections,  to  be  ap[»lied  to  the  mean  results  at 
each  hour  separately,  in  order  to  reduce  each  reading  to  the 
mean  value.  This  table  would  represent  approximately  a 
true  table  of  horary  corrections,  but  only  approximately,  un- 
less the  readings  of  the  barometer  at  the  beginning  and  end 
of  the  series  happen  to  be  the  same,  as  will  become  appa- 
rent further  on.  Finally,  if  we  api)ly  these  corrections  to 
the  original  observations,  we  Mill  have  what  has  been  called 
the  "observations  reduced."  These,  when  plotted,  show  a 
wave-like  movement  in  wjjich  uo  trace,  or  but  a  very  slight 
trace,  of  the  double  horary  oscillation  api)ears.  This  curve 
represents  very  nearly  the  abnormal  osciHation. 

It  is  very  apparent,  from  the  study  of  such  curves  plotte<l 
from  observations  reduced  to  32^  Fahrenheit,  that  there  are 
two  separate  forces  in  .u-tion,  one  j^roducing  an  oscillation 
of  regular  period,  and  the  otlier  an  irregular  but  slowly  pro- 
gressing movement  of  variable  i)eriod.  It  is  apparent,  also, 
that  during  any  twenty  four  hours,  tlie  forces  being  in  ac- 
tion together,  the  horaiy  oscilhition  will  appear  more  or  less 
distorted  or  masked  by  the  action  of  the  abnormal  move- 
ment. But  inasmuch  as  the  portion  of  the  abnormal  move- 
ment during  one  day  often  shows  approximately  a  uniform 
rise  or  fall,  the  two  coexisting  movements  can  be  easily  sepa- 
rated. Let  us  suppose  that  the  barometer  during  the  day 
had  been  rising,  and  that  it  read  two  hundred  and  forty 
thousandths  higher  at  the  end  of  the  day  than  at  tlie  be- 
ginning. If  the  abnormal  oscillation  during  that  day  had 
been  such  that  it  could  be  represented  by  a  right  line,  then 
that  portion  of  the  movement  due  to  it  would  show  a  uni- 
form vise  for  each  hour.  In  the  case  I  am  sui)[)osing,  the 
rise  in  one  hour  would  be  ten  thousandths  of  an  inch ; 
in  the  first  two  hours  twenty  thousandths,  etc.  Now,  if  we 
were  to  apply  a  correction  of  ten  thousandths  to  the  reading 
of  the  barometer  at  one  hour  after  the  initial  hour,  one  of 


17 

twenty  tbousandtbs  to  that  at  two  liours  after  the  initial 
hour,  etc.,  the  table  so  resulting  would  be  one  representing 
the  movement  of  the  barometer  freed  (entirely  iu  this  case) 
from  the  effects  of  the  abnormal  movement. 

But  it  is  very  rare  that  the  abnormal  movement  during 
the  twenty-four  hours  can  be  represented  strictly  by  a  right 
line.  It  is  usually,  when  plotted,  more  or  less  curved,  being 
a  section  of  a  sweeping  curve  which  requires  several  days 
to  pass  from  its  maximum  to  its  minimum.  Moreover,  if  it 
so  happens  that  the  time  when  the  abnormal  wave  reaches 
its  maximum  or  its  minimum  iu  the  middle  of  the  day, 
a  portion  of  that  wave  must  be  deeply  concave  and  the 
remaining  portion  convex,  and  during  that  day  the  plotted 
observations,  which  represent  the  combination  of  the  two 
movements,  will  show  an  irregular  line  different  from  the 
normal  horary  curve,  though  traces  of  that  will  probably  be 
apparent.  But  it  is  exceedingly  probable  that  during  a  se- 
ries of  ten  days  another  day  will  be  found  in  which  a  similar 
movement  of  the  abnormal  oscillation  will  occur,  but  of  such 
a  character  that  a  portion  of  it  will  show  a  concave  curve 
when  the  observations  during  a  similar  portion  of  the  other 
day  showed  a  convex  one,  and  that  the  reverse  will  occur 
during  the  remaining  portions  of  those  two  days.  That  is 
to  say,  the  abnormal  line  will  be  a  convex  curve  during  one 
day  and  a  concave  one  during  the  other.  The  combination 
of  the  observations  during  two  such  days  would  produce  a 
curve  approaching  to  a  right  line.  It  has  been  found  from 
experience  that  observation  s  taken  for  ten  days,  when  treated 
in  this  way,  generally  jiroduce  a  truthful  and  characteristic 
curve. 

This  method  of  treating  observations,  thereby  eliminating 
the  abnormal  movements,  has  been  called  the  "reduction  to 
level."  The  difference  between  the  reading  of  the  barom- 
eter at  the  initial  hour  of  two  consecutive  days  is  evidently 
the  correction  to  level  for  twenty-four  hours,  which  must  be 
2  u  B 


called  minus  when  the  barometer  during  the  day  bas  beeu 
rising,  and  plus  in  the  reverse  case,  and  the  one  twenty- 
fourth  part  of  that  is  the  correction  to  level  for  one  hour. 
The  correction  to  level  for  two  hours  is  twice  that  for  one 
hour,  etc.  When  the  correction  to  level  for  twenty-four 
hours  is  a  multiple  of  twenty-four,  the  correction  for  each 
hour  can  be  written  down  without  difficulty,  but  when  that 
is  not  the  case  it  requires  a  little  calculation  to  show  at  what 
hours  the  additions  or  subtractions  shall  be  made.  For 
example,  if  the  correction  to  level  for  one  hour  were  three- 
thousandths  of  an  inch,  the  correction  for  the  succeeding 
hours  would  be  G,  9,  12,  etc.,  thousandths  ;  but  if  it  were  a 
whole  number  of  thousandths  and  a  fraction,  as,  for 
example,  three  and  fifteen  twenty-fourths,  as  all  the  frac- 
tions less  than  half  are  to  be  thrown  away,  and  all  greater 
than  half  are  to  increase  the  whole  number  by  one,  we 
should  have  4,  7,  11,  11,  18,  22,  25,  etc.,  for  the  number 
of  thousandths  to  be  added  or  subtracted  at  8,  9,  10,  11, 
12,  1,  2,  etc.,  hours,  the  barometric  day  beginning  at  7  a.  m. 
Table  B  of  Professional  Papers  of  the  Corps  of  Engineers, 
No.  15,  is  intended  to  facilitate  the  calculations  of  the  reduc- 
tion to  level  by  showing  at  what  hours  .001  is  to  be  added 
on  account  of  the  fractional  part  of  the  correction  for  one 
hour.  This  table  I  have  found  convenient,  but  it  is  so  sim- 
ple of  construction  that  any  one  can  make  it  in  a  few  min- 
utes. 

AVheu  the  observations  reduced  to  level  are  continued 
during  several  days,  and  are  plotted,  they  show  a  series  of 
curves  occupying  different  parts  of  the  paper,  because  the 
observ^ations  at  the  initial  hour  on  different  days  will  be 
different.  "When  it  is  desirable,  as  is  often  the  case  in  prac- 
tice, to  place  them  as  nearly  as  possible  in  a  horizontal  row, 
it  is  best  to  subtract  from  each  observation  so  reduced  a  cer- 
tain number,  which  is  the  same  for  all  the  hours  of  one  day, 
but  ditiers  in  ditlterent  days,  so  as  to  make  the  observations 


19 

at  7  a.  in.  all  alike.  This  secoud  reduction,  called  "  the  reduc- 
tion to  second  level,"  does  not  change  in  the  slightest  degree 
the  character  of  the  oscillation,  but  simply  has  the  effect 
that,  when  i)lotted,  the  curves  are  found  in  a  convenient 
part  of  the  paper.  It  has  been  found  best  to  adopt  such  a 
subtrahend  for  each  day  as  will  make  the  observations  at  7 
a.  m.  a  little  less  than  any  one  in  the  series.  In  California 
29.500  is  usually  used  near  the  sea-level,  as  the  barometer 
seldom  falls  as  low  as  that. 

The  following  may  then  be  given  as  a  rule  for  obtaining 
a  table  of  horary  corrections  of  the  barometer  and  one  of 
the  abnormal  oscillations  freed  from  the  horary  movement: 

The  observations  (reduced  to  32°  F.)  are  to  be  copied  in 
such  a  way  that  all  at  the  same  hour  shall  be  placed  in  the 
same  vertical  column. 

Each  vertical  column  is  to  be  added  up  and  divided  by 
the  number  of  days  in  the  series. 

If  hourly  observations  during  the  series  are  continuous, 
the  grand  mean  is  to  be  obtained  by  adding  up  the  twenty- 
four  mean  results  at  each  hour,  and  dividing  the  sum  by 
twenty-four.  If  observations  are  not  taken  during  the  uighi 
hours,  then  an  approximate  grand  mean  is  to  be  obtained 
by  taking  the  mean  of  the  observations  at  7  a.  m.,  2  p.  m., 
and  9  p.  m. 

Subtract  the  grand  mean  from  the  mean  at  each  hour  in 
succession,  and  we  have  a  table  of  horary  corrections,  in 
which  all  those  greater  than  the  grand  mean  are  to  be  called 
minus  (  — ),  and  those  less  than  the  grand  mean,  plus  (+). 

The  table  of  horary'  corrections  being  applied  to  the  ob- 
servations at  32°  F.,  produces  the  table  of  observations 
reduced,  which  represents  the  abnormal  oscillation. 

It  is  of  great  importance,  particularly  when  the  series  is 
not  long,  that  the  observations  should  be  plotted,  in  order 
that  any  days'  observations  that  are  so  erratic  that  they 
would  evidently  vitiate  the  result  ii  they  were  combined 


20 

witii  the  otbers  cau  be  detected  aud  rejected.  The  reason 
for  this  rejection  is  that  we  cannot  expect  the  movements 
of  the  atmosphere  during  barometric  storms  to  show  its 
regular  normal  oscillation.  Another  advantage  in  plotting 
the  observations  is  to  afford  the  means  of  detecting  errors 
in  observations. 

Any  hour  of  the  twenty-four  may  be  taken  as  the  initial 
hour  of  the  barometric  day,  but  it  has  been  found  expedient, 
for  several  reasons,  to  adopt  7  a.  m.  for  that  hour.  Midnight 
is  certainly  an  inconvenient  hour,  as  observations  are  sel- 
dom taken  at  that  time.  When  observations  are  taken  but 
three  times  daily,  the  Smithsonian  hours  of  7  a.  m.,  2  p.  m., 
and  9  p.  m.  are  almost  invariably  adopted  in  this  country. 
Full  observations  taken  during  all  of  the  twenty-four  hours 
are  of  great  value  for  certain  scientific  purposes,  particularly 
in  deducing  the  laws  which  cause  the  horary  oscillation  to  be 
different  in  different  latitudes,  altitudes,  aud  climates.  But 
as  barometric  observations  for  hypsometrical  purposes  are 
seldom  taken  during  the  night,  the  practical  engineer  or 
surveyor  seldom  cares  for  them  later  than  9  p.  m.,  even 
though  he  does  not  obtain  the  night  maximum  aud  morning 
minimum,  the  first  of  which  occurs  not  far  from  midnight, 
and  the  latter  or  second  between  four  and  five  in  the  morning. 

When  the  series  is  a  short  one  aud  the  horary  table  is 
made  with  the  hope  of  obtaining  a  type  curve,  or  when  it  is 
suspected  that  the  observations,  as  usually  treated,  will  not 
give  a  result  fully  treed  from  the  abnormal  movement, 
another  horary  table  may  be  made  by  treating  the  observa- 
tions in  the  same  way,  but  adopting  7  p.  m.  as  the  initial 
hour  instead  of  7  a.  m.  If  the  series  be  of  teu  days'  dura- 
tion, the  new  table  with  the  new  initial  hour  will  produce  a 
nine  days'  series.  A  combination  of  the  two  mean  tables  is 
more  likely  to  produce  a  good  horary  curve  than  either  one 
separately.  This  would  be  naturally  the  case,  for,  from  the 
very  principle  of  the  reduction  to  level,  it  is  assumed  that 


21 

the  portion  of  the  abnormal  wave  during  each  day  is  a  right 
line,  whereas  it  is  only  approximately  so,  and  is  in  reality  a 
curve  more  or  less  convex  or  concave.  Now,  by  adopting 
another  initial  hour  an  additional  horary  table  can  be  made, 
and  it  is  more  than  likely  that  by  the  combination  of  the 
two  the  abnormal  movement  is  more  thoroughly  eliminated 
When  the  series  of  hourly  observations  is  not  continuous 
as,  for  instance,  when  the  night  observations  are  not  taken, 
we  cannot  use  the  method  just  given,  but  we  must  adopt 
some  method  of  obtaining  approximately  a  grand  mean,  and 
it  has  been  found  that  the  mean  of  7  a.  m.,  2  p.  m.,  and  9 
p.  m.,  gives  a  close  approximation  to  the  mean  of  the 
twenty-four  hourly  observations.  It  is  important  to  know 
how  close  the  agreement  is.  Although  the  number  of  sta- 
tions where  I  have  been  able  to  collect  observations  is  quite 
small,  still  they  have  been  sufficient  to  prove,  not  only  that 
the  difference  in  obtaining  the  daily  mean  pressure  by  the 
two  methods  is  not  great,  but  that  it  varies  by  a  regular 
law  during  the  months  of  the  year.  Tliis  is  shown  by  the 
following  table : 


22 


«   S 

c 

1 

o 

1 

o 
o 
o 

o 

1 

o 
o 

c 

i 

-1     o 

8  8 

o 

1 

c 
o 

1 

Q 

s  s  § 

o   o    o 

+  +  + 

-J.    o    --    —    o 
o    o    o    o    o 
o    c    o    o    o 

+  1  +  + 

O      11 

^^    o 
o    o 

+  + 

s  §  s 

o    o   o 

-f  1  + 

2  S  S  S  g 

o    o    o    o    o 

+  +  +  1  + 

3  8 

O 

§  g  s 

o    o    o 

'  +  1 

o    o    o    o    o 
o    o    o   o    o 

+  +  1   1   1 

o   o 

8  8 

a  . 

§  s  § 
l"  1  + 

O 
1 

«     (»     (N     — 1     — 

8  §  §  §  g 
1*  i  \    \    \ 

2  S 

o    o 

D 

to 

n    n    o    ^    n 
o    o    o    o    o 
c    o    o    o    o 

l'     f      *     l"     1 

O 
1 

■«i>    •"J-    m    (M    o» 

g  §  8  §  § 

l"   l'  l'  l'   l' 

00   n 
o   o 

l"  l' 

1-2 

oooooooooooo 
oooooooooooo 

l'   1    1*   1    1    1    1    1    1    I    f   1 

o   o 

1    1 

2 

■^    ^    rt 
o    o    o 
coo 

l'   l'  l' 

»r;    ^    c«    •-    "^ 
o    o    o    o    o 
o    o    o    o    o 

l'  l"  f  l"   l" 

o   o 

1    1 

1 

•j:     ■»     O 

o    o    o 
o     o     = 

l'  l'   l' 

s  s  s  §  s 

o    o    o    o    o 

l'   l"   l'  f  + 

§  2 

o   o 

l"   l' 

<1 

L-5      ffJ     t= 

e^    o    o 
o    o    o 

l'   1    l" 

t-    <N    (J*    r»    m 

o    o    o    o    o 
o    o    o   o   o 

l'  l'  l"  l'  1 

SI    n 

§  8 
1    l' 

1 

n    ffi    t» 

o    o    o 
o    o    o 

+  +  i 

—      CJ      (»     —     « 

o    o    o    o    o 
o    o    o    o    o 

l'  +  l'  l'  l' 

g  i 

o   c 

1 

M     CO     /-> 

§  §  i 

1  +  r 

-^     rt     o     o     — ■ 

o    o    o    o    o 
o    o    o    o    o 

+  +■  "  -f 

8  o 

o    o 

+  + 

^2 

o    o    S    S    o    o 
o    o   §   o   o    o 

g  g  s  s  § 

c    o    o    O    o 

+  +  +  +  + 

o    n 

2  8 
+  + 

o5 

a 
2 

z 

< 

1 

z 

c 

E- 

c 

11 
11 

J 

> 

t- 

!- 

>  "i 
i  1 

H     5 

1 

-.  _a 
> 

■    c 

•J 
J     c 

c 
t 

c 

1 

a      , 

«    : 

a    -1 

i  i 

C  C2 

B 
e 

23 

By  examining  the  table,  it  will  be  seen  that  out  of  the  107 
differences  in  the  monthly  results  by  the  two  methods  there 
is  one  amounting  to  tea  thousandths  of  an  inch  of  the 
barometric  column  in  the  stormy  mouth  of  December,  one 
of  seven  thousandths,  six  of  six  thousandths,  four  of  five 
thousandths,  sixteen  of  four  thousandths,  and  all  the  rest 
are  less  than  that  amount.  In  fact,  out  of  the  107  results 
there  are  only  twelve  in  which  the  differences  are  so  great 
as  five  thousandths.  The  mean  results  show  that  the  mean 
of  observations  at  7  a.  m.,  2  p.  m.,  and  9  p.  m.  is  less  than  the 
mean  of  twenty-four  hourly  observations  in  the  months  of 
November,  December,  January,  and  February,  the  January 
results  giving  a  difference  of  three  thousandths  of  an  inch, 
and  that  in  the  midsummer  months  it  is  greater  by  the 
same  amount.  In  March  and  October  there  is  no  difference. 
The  yearly  mean  difference  by  the  two  methods  is  less  than 
one-thousandth  of  au  inch.  The  above  table  can  be  used 
as  a  table  of  corrections  to  be  applied  to  observations  taken 
in  any  month  in  order  to  reduce  them  to  the  yearly  mean. 

This  table  has  been  deduced  from  monthly  means,  and  it 
is  not  to  be  supposed  that  observations  taken  in  a  single 
day,  or  even  a  series  of  a  few  days'  duration,  will  afford  so 
close  an  accord  by  the  two  methods.  There  is,  however,  a 
method,  when  the  observations  are  taken  at  the  Smithso- 
nian hours,  which  affords  a  very  good  value  for  the  daily 
mean,  as  compared  with  the  mean  of  twenty-four  observations 
in  a  day  beginning  at  7  a.  m.  It  is  to  take  the  mean  of  7 
a.  m.,  2  p.  m.,  9  p.  m.,  and  7  a.  m,  of  the  succeeding  day 
and  apply  to  it  a  correction,  so  as  to  reduce  it  to  what  it 
would  have  been  had  the  observations  been  taken  strictly 
at  eight  hours  apart.  From  7  a.  m.  to  2  p.  m.  is  an  interval 
of  but  seven  hours,  and  from  7  a.  m.  to  9  p.  m.  is  14  hours. 
Hence  the  sum  of  these  four  observations  is  too  small  by 
the  rise,  or  too  great  by  the  fall,  between  2  p.  m.  and  3  p. 
m.,  together  with  the  rise  or  fall  between  9  p.  m.  and  11  p. 
m,;  that  is  to  say,  during  three  hours.  But  3  hours  is  one- 
eighth  of  a  day,  in  which  day  the  barometer  had  au  average 


24 

rise  or  fall  measured  by  the  amouut  which  has  been  called 
"the  correctiou  to  level  for  twenty-four  hours,"  aud  which 
is  the  difference  in  the  readings  of  the  barometer  at  7  a.  m. 
on  one  day  and  7  a.  m.  on  the  next.  Therefore  one  eighth 
of  that  amount  should  be  applied  as  a  correction  to  the 
sum  of  the  four  observations  in  question,  so  as  to  increase 
that  sum  when  the  barometer  for  the  day  had  been  rising 
and  diminish  it  when  falling.  It  must  be  borne  in  mind, 
however,  that  this  correction  is  to  be  applied  to  the  "ob- 
servations reduced,"  or,  in  other  words,  to  tiie  observations 
after  the  horary  correction  had  been  applied. 

We  may  therefore  have  the  following  rule  for  obtaining 
the  mean  daily  pressure  from  four  such  "  observations  re- 
duced," the  barometric  day  commencing  at  7  a.  m.  Take 
the  sum  of  the  observations  so  reduced  at  7  a.  m.,  2  p.  m., 
9  p.  m.,  and  7  a.  m.  the  next  morning  and  apply  to  it  one- 
eighth  of  the  difference  between  the  observations  at  the 
beginning  of  the  two  consecutive  days,  calling  the  difference 
2)lus  (-J-)  when  the  barometer  for  the  day  had  been  rising 
and  mimis  (— )  in  the  reverse  case,  then  divide  the  result 
by  four,  and  we  have  the  required  daily  mean. 

As  it  is  desirable  to  have  a  definite  idea  of  the  difference 
between  the  daily  barometric  means  as  computed  from 
twenty-four  hourly  observations  and  that  given  by  the  last 
described  method,  and  also  between  the  former  and  that 
from  observations  taken  at  7  a.  m.,  2  p..  m.,  and  9  p.  m.,  I 
present  a  table  from  ten  days'  observations  at  Sacramento, 
Placerville,  Strawberry  Valley,  and  Hope  Valley,  taken 
during  August,  18G0.  The  upper  line  of  each  group  gives 
the  difference  between  the  daily  mean  as  calculated  from 
twenty-four  hourly  observations  aud  the  mean  of  7  a.  m.,  2 
p.  m,,  9  p.  m.,  aud  7  a.  m.  the  next  morning,  corrected  as 
above  described.  The  lower  line  gives  the  difference  between 
the  first  and  the  mean  of  7  a.  m.,  2  p.  m.,  and  9  p.  m.  It  will 
be  seen  that  the  amount  of  variation  from  the  mean  of  twenty- 
four  hourly  observations  is  nearly  three  times  greater  by  the 
last  mentioned  method  than  by  the  first. 


25 


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26 

In  almost  every  iustauce  it  is  shown  that  the  second 
method  gives  results  much  nearer  the  mean  of  twenty-four 
hourly  observatioDS  than  the  third,  which  is  a  simple  mean 
of  the  observations  at  7  a.  m.,  2  p.  m.,  and  9  p.  ra.  Taking 
the  mean  of  twenty-four  hourly  observations  as  the  stand- 
ard, and  taking  the  difterence  between  this  standard  and 
the  results  given  by  the  other  two  methods,  we  find  that 
the  sum  of  these  differences  in  a  ten  days'  series  by  the 
method  of  four  observations  so  reduced  is  only  38  per  cent, 
of  the  corresponding  amount  obtained  from  a  simple  mean 
of  the  observations  taken  at  7  a.  m.,  2  p.  m.,  and  9  p.m. 5  and 
the  maximum  errors  are  in  proportion,  they  being  at  Sac- 
ramento .007  in.  and  .032  in.,  and  at  Hope  Valley  .008  in. 
and  .030  in.  As  this  method  of  obtaining  the  barometric 
mean  involves  very  little  additional  trouble  after  the  obser- 
vations have  been  actually  taken,  it  appears  to  me  worthy 
of  being  adopted.  For,  in  the  field,  we  cannot  tell  when 
the  atmospheric  conditions  which  cause  the  difference 
between  the  two  methods  are  in  operation,  and  when  the 
maximum  difi'erence  will  occur ;  hence  the  results  are  apt 
to  be  considered  untrustworthy  up  to  the  limit  of  the  maxi- 
mum error.  On  the  other  hand,  if  that  maximunj  error  can 
be  reduced  two-thirds  or  one-half,  the  results  can  surely  be 
relied  upon  within  the  smaller  limit. 

Although  observations  at  the  Smithsonian  hours  have 
been  shown  to  give  a  close  approximation  to  the  mean  of 
twenty-four  hourly  observations,  still  other  hours  have  been 
adopted  that  give,  also,  very  good  results.  The  Coast  Sur- 
vey adopted  long  ago  the  mean  of  0  a.  m.,  noon,  and  6  p. 
m.  as  a  good  barometric  mean,  though  latterly  they  have 
adopted  the  hours  of  7  a.  m.,  2  p.  m.,  and  9  p.  m.  I  have 
obtained  from  Louis  Wilson,  tidal  observer  at  Astoria, 
Oregon,  the  following  table,  which  explains  itself: 


27 


28 

This  table  shows  nearly  as  good  results  as  from  observa- 
tions at  the  Smithsonian  hours,  but  as  the  latter  hours  have 
been  so  universally  adopted,  and  it  is  very  desirable  to  have 
uniformity  in  the  hours  of  observation,  so  that  comparisons 
can  be  easily  made,  I  would  recommend  that  the  Smith- 
sonian hours  be  adhered  to  in  future  observations  where 
they  are  taken  but  three  times  a  day. 

Having  explained  how  the  horary  correction  of  the  barom- 
eter can  be  obtained  from  a  short  series  of  observation,  I 
now  wish  to  point  out  certain  facts  concerning  this  oscilla- 
tion. It  has  been  found  that  when  the  stations  are  near  the 
sea  level,  the  curves  for  each  month  at  different  localities 
are  of  the  same  character,  the  critical  hours  occurring  at 
the  same  times,  but  varying  in  range  or  amplitude,  the 
warmest  localities  giving  the  largest  curves.  Hence,  as  a 
general  rule,  the  curves  are  smaller  as  the  latitude  increases. 
But  in  the  same  latitude  and  climate  the  curves  for  the  dif- 
ferent months  are  different.  They  vary  in  the  hours  of 
maxima  and  minima,  and  also  in  the  amplitude  of  the  oscil- 
lation. While  the  hour  of  the  morning  maximum  does  not 
materially  vary  during  the  different  months,  that  of  the 
afternoon  varies  with  the  seasons,  being  usually  between 
2  and  3  p.  m.  in  midwinter  and  between  5  and  G  p.  m* 
in  midsummer.  The  consequence  of  this  is,  that  if  the 
tables  representing  the  hourly  observations  taken  in  Jan- 
uary and  July  are  subtracted  the  one  from  the  other  and 
this  difference  plotted,  it  gives  a  curve  nearly  as  great  as 
is  produced  from  either  set  of  observations.  But  as  soon 
as  the  element  of  altitude  enters  into  consideration,  the 
curve  changes  materially,  and  according  to  a  law  which  has 
not  yet  been  discovered.  As  a  general  rule,  the  curves  for 
high  altitudes  are  quite  small.  At  the  Grand  Saint  Ber- 
nard, that  portion  of  the  midsummer  curve  for  the  hours 
when  the  sun  is  above  the  horizon  is  exceedingly  minute, 
while  the  night  portion  of  the  curve  presents  an  oscillation 


29 

of  about  0.040  inch.  Near  the  summit  of  the  Sierra  Nevada 
iu  July  and  August,  the  moruing  maximum  is  at  7  a.  m., 
while  in  the  valley  below  it  is  at  11  a.  m.  There  is  no  sim- 
ilarity between  the  Grand  Saint  Bernard  curves  and  those 
of  the  Sierra  Nevada,  though  the  altitudes  of  the  two  sta- 
tions do  not  diifer  materially.  If  we  had  a  series  of  stations 
one  thousand  feet  apart,  vertically,  from  the  sea  level  to  the 
summit  of  the  mountain,  we  would  find  that  the  curves  at 
all  the  stations  would  be  different. 

The  amplitude  of  this  oscillation  iu  the  temperate  zone 
usually  varies  from  0.010  in.  to  O.OSO  in.  Near  the  equator 
the  oscillation  is  greater,  amounting  to  nearly  0.120  in., 
and  the  abnormal  oscillation  being  there  very  small,  the 
horary  oscillation  is  so  regular,  that  the  hour  of  the  day  can 
be  ascertained,  at  least  approximately,  from  the  reading  of 
the  barometer.  But  the  abnormal  oscillation  seems  to  in- 
crease with  the  latitude,  while  the  horary  movement  becomes 
less,  and  iu  high  latitudes  the  latter  is  so  masked  by  the 
former,  that  a  long  series  of  observations  is  required  to  ob- 
tain a  reliable  horary  curve. 

From  the  above  facts  it  becomes  apparent  that  the  effects 
of  this  horary  oscillation  ought  to  be  neutralized  in  some 
way.  The  computed  differences  of  altitude  from  observa- 
tions taken  at  different  hours  are  different  on  account 
of  the  oscillations  at  the  lower  and  upper  stations  being  so 
entirely  differeut.  Now,  as  a  change  of  0.001  in.  in  the 
barometer  at  one  station  will  affect  the  result  about  a  foot, 
unless  a  corresponding  change  occurs  at  the  other  station, 
it  is  apparent  that  we  should  correct  the  observations  before 
they  are  used  in  the  determination  of  altitudes,  so  as  to 
eliminate  the  effect  of  the  horary  movement.  The  follow- 
ing general  conclusions  are  giv^eu  in  Professional  Papers  of 
the  Corps  of  Engineers,  No.  15,  together  with  a  large  num- 
ber of  horary  tables  and  curves: 

1st.  As  the  value  of  the  principal  term  of  the  barometric 


30 

formula  depends  upon  the  difference  between  the  readings 
of  the  barometers  at  an  upper  and  lower  station,  and  as 
the  horary  oscillation  of  the  barometer  is  quite  different  at 
the  two  stations  when  the  difference  of  altitude  is  at  all 
considerable,  and  as  its  amount  is  often  sufQcient  to  cause 
considerable  error  in  hypsometrical  calculations  if  neglected, 
even  when  the  observations  at  the  two  stations  are  simul- 
taneous, it  is  important  to  eliminate  it  as  far  as  practicable. 

2d.  As  the  horary  curves  and  tables  for  any  two  days, 
even  in  a  short  series,  are  not  identical,  the  best  way  to 
eliminate  the  effect  of  this  oscillation  is  to  use  the  mean  of 
observations  taken  at  short  intervals,  as,  for  instance,  hourly, 
for  one  day,  or  for  a  number  of  wJiole  days,  the  day  com- 
mencing at  any  convenient  hour. 

3d.  When  this  is  impracticable,  and  when  the  horary 
tables  for  the  station  and  month  are  previously  known,  and 
the  observations  are  for  a  portion  of  a  day  only,  or  for  por- 
tions of  several  days,  the  horary  correction  should  be 
applied  to  them  before  they  are  used  in  estimating  differ- 
ences of  altitudes. 

4th.  When  the  horary  tables  for  one  or  both  stations  are 
unknown,  and  hourly  observations  cannot  be  taken,  the 
aim  should  be  to  obtain  the  nearest  approximation  to  a 
daily  mean.  For  this  purpose,  the  mean  of  observations 
taken  at  7  a.  m.,  2  p.  m.,  and  9  p.  m.,  or  of  6  a.  m.,  2  p.  m., 
and  10  p.  m.,  or  6  a.  m.,  noon,  and  6  p.  m.  have  been  found 
to  afford  quite  good  results. 

ON  THE  VARIATIONS  IN  TEMPERATURE. 

While  the  horary  barometric  oscillation,  when  freed  from 
the  abnormal  movement,  does  not  vary  much  from  day  to 
day  at  the  same  station  during  a  short  series,  it  is  very  dif- 
ferent with  the  corresponding  thcrmometric  oscillation.  In 
the  one  case  it  is  small  as  compared  with  the  abnormal  one, 
and  so  nearly  uniform  in  character  that  a  mean  of  a  few  days' 


31 

observations,  properly  treated,  will  give  a  characteristic 
horary  table  aud  curve  for  that  station  and  month;  and,  by 
elimination,  the  abnormal  wave  can  be  represented.  In  the 
case  of  the  temperature,  the  horary  movement  is  very  large 
as  compared  with  the  other,  and  varies  so  much  from  day  to 
day  that  no  characteristic  horary  table  can  be  used  in  elimi- 
nating this  movement,  and  obtaining  an  abnormal  ther- 
mometric  wave;  though  the  curve  is  a  simple  one,  having 
but  one  maximum  and  one  minimum  in  24  hours,  still  the 
range,  or  vertical  amplitude,  may  be  several  times  as  great 
in  one  day  as  in  another  during  a  series  of  ten  days.  The 
consequence  is  that  the  method  of  separating  the  two  move- 
ments, which  we  have  found  practicable  with  the  baromet- 
ric observations,  is  not  applicable  to  those  with  the  ther- 
mometer. 

While  the  barometer  gives  us  a  measure  of  the  weight  of 
the  whole  column  of  air  over  the  place  of  observation,  the 
thermometer  is  local  in  its  character  and  affected  by  every 
pufi'  of  wind  that  blows  over  it.  It  is  true  that  there  is  one 
paramount  influence  which  i)roduces  a  horary  thermometric 
oscillation  with  one  decided  maximum  and  one  minimum, 
the  former  usually  occurring  between  2  and  4  p.  m.  and  the 
latter  about  one  hour  before  sunrise;  but  the  amount  of 
variation  during  the  day  is  greatly  modified  by  many  acci- 
dental causes,  such  as  the  clearness  or  cloudiness  of  the 
atmos[)here,  the  direction  and  force  of  the  wind,  the  rapid- 
ity or  slowness  of  the  evaporation  or  condensation  of 
aqueous  vapor,  and  many  other  local  meteorological  phe- 
nomena. For  these  reasons  the  amount  of  this  oscillation 
must  vary  greatly  from  day  to  day,  and  this  experience 
shows  us  to  be  the  case. 

If,  in  a  series  of  ten  days'  observations,  the  horary  ther- 
mometric oscillations  are  plotted,  it  will  almost  always  be 
found,  in  temperate  latitudes,  that  the  vertical  range  in  the 
curve  for  some  one  day  will  be  twice  as  great  as  for  another 


32 

in  that  short  series,  aud  it  is  not  unusual  to  find  that  the 
difference  is  three  and  even  four  times  as  great.  It  is  this 
great  difference  in  range  from  day  to  day  which  prevents 
us  from  using  advantageously  a  mean  horary  thermometric 
table  for  hypsometrical  purposes.  The  same  reason  which 
makes  it  necessary  to  eliminate  the  effects  of  the  horary 
oscillation  of  the  barometer  applies  with  still  greater  force 
to  the  varying  temperature.  It  is  principally  by  means  of 
the  pressure  at  the  two  stations,  in  connection  with  the 
corresponding  temperature,  that  we  are  to  obtain  the  dif- 
ference of  altitude  between  them.  If  the  change  in  temper- 
ature from  hour  to  hour  caused  a  proper  corresponding 
change  in  the  height  of  the  barometer,  we  could  disregard 
the  effects  of  the  horary  oscillations  altogether  and  use  the 
observed  pressure  and  temperature  at  the  two  stations. 
But  this  is  not  so.  When  we  take  twenty -four  hourly  ob- 
servations of  the  barometer  and  thermometer  at  stations  of 
considerable  difference  of  altitude,  and  estimate  the  verti- 
cal distance  between  these  stations  by  the  formula,  using 
successively  each  pair  of  corresponding  observations,  we 
have  a  series  of  twenty-four  numbers  far  from  being  alike. 
Again,  when  we  do  the  same  with  the  next  two  sets  of 
twenty-four  observations  taken  during  the  next  day,  we 
have  another  series  differing  from  the  first,  and  it  would  be 
very  materially  different  if  the  horary  theimometric  oscilla- 
tions for  the  two  days  are  quite  different,  as  they  are  apt  to 
be.  For  these  reasons  it  is  evident  that  the  horary  oscilla- 
tions of  both  the  barometer  and  thermometer  must  be  elim- 
inated before  the  observations  can  be  properly  used  in  esti- 
mating differences  of  altitude.  Yet  I  believe  it  is  a  common 
practice  with  computers  to  use  the  observed  air  tempera- 
ture. 

When  hourly  observations  of  the  thermometer  are  taken, 
aud  the  monthly  mean  for  the  different  months  are  obtained, 
it  has  been  found  that  the  range  of  the  horary  thermomet- 


33 

lie  oscillation  varies  from  montli  to  moutli,  the  same  be- 
ing greatest  in  the  hottest  months  and  least  in  the  coldest. 

The  (litfereuce  in  these  ranges  seems  to  be  greatest  when 
the  (lilierence  between  the  mean  temperatures  of  the  hottest 
and  coldest  month  is  gre;itest.  The  range  is  usually  great- 
er ill  arid  districts  than  in  thu  more  humid  ones  near  the 
sea.  It  has  been  found  from  observations  at  stations  vary- 
ing in  altitude  from  the  sea  level  to  the  summit  of  the 
Sierra  Nevada,  that  in  Angust  the  range  at  Sacramento, 
near  sea  level,  was  17  degrees;  at  Placerville,  about  2,000 
feet  high,  it  was  31  degrees;  at  Strawberry  Yalley,  al)out 
5,700  feet  high,  it  was  33  degrees ;  and  at  Hope  Valley, 
7,000  feet  high,  it  was  17  degrees.  In  January,  at  the  same 
stations,  the  range  was  11  degrees  at  Sacramento,  17.}  de- 
grees at  Placerville,  10^  degrees  at  Strawberry  Valley,  and 
17  degrees  at  Hope  Valley.  It  therefore  by  no  means  fol- 
lows that  the  range  of  this  oscillation  diminishes  with  the 
altitude,  though  it  is  doubtless  samll  at  exceedingly  high 
places. 

It  is  evident  from  the  preceding  remarks  that  the  ques- 
tion of  how  best  to  obtain  the  daily  mean  tem[)erature,  in 
order  to  secure  good  hypsoiuetrical  results,  is  of  great  im- 
portance. Fortunately,  this  is  not  difficult.  With  the  ba- 
rometer the  daily  mean  can  only  be  ascertained  from  obser- 
vations taken  during  that  day  at  the  precise  locality,  or 
ai)proximately  so,  by  applying  a  horary  correction  But 
with  the  thermometer  the  case  is  different.  As  the  tempera- 
ture during  a  day  is  nearly  the  same  over  a  large  area  in  a 
level  country,  observations  can  usually  be  taken  in  the 
field  at  7  a.  m.,  2  p.  m.,  and  9  p.  m.,  and  a  good  mean  value 
to  the  temperature  of  the  day  thus  obtained,  ahhough  the 
party  has  been  in  motion.  It  the  party  has  been  in  an  un- 
even or  mountainous  region,  then  the  only  way  is  to  assume 
that  the  mean  daily  temperature  varies  three  degrees  with 

each  thousand  feet  of  difference  of  altitude.     I  am  aware 
3  u  B 


34 


that  this  rule  gives  but  a  very  rude  approximatiou  to  the 
truth,  but,  except  when  the  change  in  altitude  from  camp  to 
camp  is  very  great,  the  error  from  adopting  it  will  be  small. 
The  following  table  gives  a  comparison  between  monthly 
mean  temperatures  obtained  by  twenty -four  hourly  obser- 
vations and  the  mean  of  those  taken  at  7  a.  m.,  2  p.  m., 
and  9  p.  m. : 


35 


■2  a 


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5"-= 


r    S  35 


■2  ^ 


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I     I 


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36 

It  will  be  seen  that  tbemeau  temperature  of  7  a.  m.,  2  p.  m., 
aud  9  p.  m.,  at  almost  every  station,  gives  a  result  too  great,  in 
every  montb,  as  compared  witli  the  mean  of  twenty-four  hourly 
observations ;  but  the  difference  is  not  great,  seldom  exceed- 
ing in  any  one  month  one  and  one-half  degrees.  The  mean 
results  show  that  the  mean  temperature  thus  ob  tained  by 
the  two  methods  most  nearly  agrees  in  December,  where  the 
difference  is  less  than  one-quarter  of  a  degree,  an  d  that  the 
difference  is  greatest  in  June.  From  December  to  June  the 
difference  increases  with  much  uniformity,  and  from  June 
to  December  it  decreases  in  the  same  manner ;  so  that  if  the 
table  "were  i^lotted  it  would  show  a  smooth  curve.  This 
table  can  be  used  as  a  table  of  corrections,  to  be  applied  to 
observations  taken  at  7  a.  m.,  2  p.  m.,  and  9  p.  m.,  in  order 
to  reduce  them  to  the  mean  of  twenty-four  hourly  observa- 
tions. 

I  next  present  a  table  of  comparison  between  the  means 
of  thermometric  observations  taken  at  7  a.  ra.,  2  p.  m.,  and 
0  p.  m,  aud  that  of  those  taken  at  0  a.  m.,  noon,  and  6  p. 
m.  They  were  furnished  me  by  Louis  Wilson,  tidal  obser- 
ver at  Astoria,  Oreg.,  and  are  for  three  years. 


37 


5  '^ 


S  s 

i     ^ 


1 

o 

1 

O  O  i 

1  1 

d 
1 

-^   r-   O 

o  o  o 

1   1   1 

d 
1 

CI  c^  o 

o  o  o 

1  1  1 

d 

1 

C»   ^   rH 

o  o  o 

1  1  1 

d 
1 

s  . 

■<?•  CJ  o 

o  o  o 

1  1  1 

d 
1 

-5 

O  CI   =5  1  O 

o  o  o  1  o 

1  1  1  1  1 

•^ 

05  t-  O 

O  O  rn" 

1    1    1 

d 

1 

2 
^ 

00   L-   1- 

o  o  o 

1  1  1 

d 
1 

CO 

d 
1 

in  r^  o» 
o  o  o 

1  1  1 

< 

*?"  in  '^ 
o  o  o 

1  1  1 

o 

1 

Maicb. 

—  0.5 

—  0.1 

—  0.2 

n 
d 

1 

o 
d 

1 

3 
u 

c5  o  o 
+  i   1 

5 

3 

a 

O  ^  St 

o  o  o 

1  1  + 

o 
d 

1 

1 

i 

o  -^ 

00  TO 

1 

38 

It  appears  from  this  table  that  while  the  winter  months 
give  results  which  agree  almost  exactly  by  the  two  methods, 
the  results  in  the  summer  months  differ  by  about  three- 
quarters  of  a  degree,  the  mean  of  G  a.  m.,  noon,  and  C  p.  m. 
being  the  greater.  As  in  those  months  the  mean  of  7  a.  m., 
2  J).  111.,  and  9  p.  m.  gives  results  too  great  by  about  that 
amount  as  compared  with  the  mean  of  twenty-four  hourly 
observations,  it  follows  that  the  other  method  must  be  con- 
sidered decidedly  inferior. 

From  an  examination  of  the  monthly  mean  temperatures 
from  year  to  year  at  Geneva  and  the  Grand  St.  Bernard  it 
has  been  found  that  when  at  one  station  the  monthly  mean 
temperature  departs  considerably  from  that  determined  by 
the  mean  of  a  long  series,  it  is  not  local,  for  the  same  depart- 
ure is  found  at  the  other  station. 

OF  HYPSOMETRICAL  RESULTS  FROM  DAILY  MEANS. 

It  is  presumed  that  the  reader  understands  the  barometric 
formula,  and  therefore  but  few  remarks  concerning  it  are 
necessary  here.  The  most  important  parts  of  it  are  the 
pressure  and  temperature  terms.  The  first  consists  of  a 
constant,  multiplied  by  the  difference  between  the  logarithms 
of  two  numbers,  which  are  the  readings  of  the  barometer  at 
a  lower  and  an  upper  station.  The  second  term  is  the  pro- 
duct of  the  former  divided  by  900  and  multiplied  by  the 
sum  of  two  numbers,  which  sum,  when  the  Fahrenheit  scale 
is  used,  is  the  sum  of  the  readings  of  the  open-air  thermom- 
eter at  the  two  stations,  diminished  by  64,  which  is  twice 
the  temperature  at  the  freezing-point. 

The  other  terms  of  the  formula  are  usually  comparatively 
small,  though  by  no  means  to  be  disregarded  in  the  com- 
putations. When  the  formula  is  api^lied  to  observations 
taken  for  some  time  at  the  same  two  stations  (in  wiiich  case 
the  true  difference  of  altitude  between  them  will,  of  course, 
be  constant),  the  values  of  these  terms  should  be  constant. 


30 

With  such  a  series,  the  mean  readings  of  the  barometers 
and  thermometers  can  be  used  to  compute  the  mean  differ- 
ence of  altitude  between  them.  When  this  is  done,  and  the 
value  of  those  small  terms  is  once  determined,  jf  separate 
computations  are  made  to  obtain  the  difference  of  altitude 
from  each  day's  observations,  the  same  value  for  the  sum 
of  these  small  terms  can  be  used,  thus  avoiding  much  use- 
less labor  in  computing.  When  the  pairs  of  stations  are 
different,  separate  calculations  must  be  made  to  obtain  the 
values  of  these  terms,  which  can  be  conveniently  done  by 
the  aid  of  the  tables  in  the  appendix  to  Professional  Papers 
of  the  Corps  of  Engineers,  No.  15,  before  mentioned. 

If  computations  are  made  from  the  daily  means  of  ob- 
servations during  every  day  in  a  month  at  the  same  two 
stations,  each  resultjjwill  vary  more  or  less  from  the  monthly 
mean.  If  a  table  of  wanderings  from  the  mean  is  made, 
some  of  the  numbers  will,  of  course,  be  greater  and  some 
less  than  the  mean,  and  should  be  written,  some  with  a  plus 
(-f)  and  some  with  a  minus  (  — )  sign.  If  all  these  errors 
or  wanderings  are  added  together,  without  regard  to  sign, 
and  divided  by  the  number  of  days  in  the  month,  the 
resulting  number  will  give  the  mean  error;  and  it  may  be 
confidently  assumed  that  if  similar  observations  at  those 
two  stations  are  taken  during  the  same  month  of  another 
year,  very  similar  results  will  be  obtained.  But  it  can  be 
shown  from  a  large  number  of^computed  differences  of  alti- 
tude from  daily  means  that  the  amounts  of  the  maximum 
and  mean  errors  in  different  months  at  the  same  two  stations 
vary  considerably,  being  least  in  mid-summer  and  greatest 
in  mid-winter. 

As  a  general  rule,  when  the  difference  of  altitude  between 
the  two  stations  is  at  all  considerable,  the  amounts  of  the 
maximum  and  mean  errors  vary  with  the  difference  of  alti- 
tude. This  is  quite  natural,  for,  in  the  first  place,  when  the 
difference  of  altitude  is  great  the  horizontal  distance  between 


40 

tliem  must  also  be  coin[)aratively  great,  and  tbe  errors  are 
apt  to  be  greater  tbau  when  the  stations  are  close  together ; 
but,  in  the  second  place,  the  temperature  term  of  the  form- 
ula is  the  i)rodact  of  the  approximate  difference  of  altitude 
given  by  the  pressure  term  multiplied  by  a  variable  depend- 
ing upon  the  temi)erature.  Now,  the  value  of  this  variable 
being  different  from  day  to  day,  the  wanderings  from  the 
mean  value  of  the  temperature  term  are  inevitable,  and 
must  be  proportional  to  the  value  of  this  variable,  as  well 
as  to  the  difference  of  altitude.  This  last  cause  of  error, 
however,  does  not  materially  affect  the  result  when  the 
difference  of  altitude  is  quite  small,  in  which  case  the  errors 
are  apt  to  vary  with  the  horizontal  distance  between  the 
stations. 

The  following  tables  of  maximum  and  mean  errors  in  com- 
l)utiug  differences  of  altitude  from  daily  means  are  now 
presented.  They  are  the  result  of  great  labor,  as  every  two 
corresponding  numbers  are  the  result  of  as  many  different 
computations  as  there  were  days  in  the  month ;  but  they 
give  a  clear  idea  of  the  j)robable  amount  of  error  to  which 
such  results  are  liable. 


41 


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43 

From  the  examiuatiou  of  a  large  lumiber  of  observatious 
and  computed  results  from  daily  means,  I  have  come  to  the 
conclusion  that  there  is  no  relation  between  the  height  of 
the  barometer  at  the  lower  or  upper  station  and  the  value  of 
the  differences  of  altitude.  That  is  to  say,  the  wandering 
from  the  monthly  mean  may  be  a  maximum  or  a  minimum 
with  either  a  high  or  a  low  barometer. 

The  cause  of  erratic  results  from  daily  means  must  be 
attributed  to  the  fact  that  the  atmosphere  is  seldom,  if  ever, 
in  a  state  of  equilibrium,  and  hence  the  wanderings  cannot 
be  controlled  by  any  law,  and  must  be  incident  to  all 
measurements  of  this  kind. 

OF  THE  VARIATIONS  IN  HYPSOMETRICAL  RESULTS 
FROM  MONTHLY  MEANS. 

When  observations  of  the  barometer  and  thermometer 
have  been  continued  for  a  number  of  years  at  two  stations, 
and  the  mean  monthly  readings  are  used  in  computing 
the  difference  of  altitude  between  them,  it  has  been  ascer- 
tained that  these  computed  results  from  observations  taken 
in  the  different  months  differ.  If  we  take  the  series  of  25 
years  at  Geneva  and  the  Grand  St.  Bernard  as  affording  us  the 
best  tj'pe  series  available,  we  find  that  the  computed  differ- 
ence of  altitude  for  the  month  of  December  and  July  differ 
by  101  feet,  and  that  those  for  the  different  months  vary  by 
a  definite  law,  so  that  when  plotted  they  show  a  smooth 
curve.  We  can  only  ascertain  what  this  law  is  bj'  compar- 
ing results  from  observations  taken  in  different  latitudes, 
altitudes,  and  climates.  Unfortunately,  extensive  series  of 
reliable  observations  at  high  and  low  altitudes  are  seldom 
to  be  found.  But  I  shall  make  use  of  such  as  I  have  had 
access  to,  and  from  which  some  important  facts  can  be  de- 
duced. 

Going  back  to  the  observations  at  Geneva  and  the  Grand 
St.  Bernard,  the  first  fact  of  importance  is,  that  while  the 


44 

25  years'  series  gives  a  good  curve,  the  observations  taken 
in  any  one  year  do  not,  and  the  plotted  results  from  monthly 
means  of  observations  taken  during  a  single  year  are  so 
irregular  that  it  would  be  difficult  to  develop  from  them 
a  law  in  this  variation.  This  fact  shows  that  even  with 
these  stations,  if  a  table  of  corrections  were  made  to  reduce 
the  results  taken  during  each  of  the  mouths  to  the  mean 
for  the  year,  and  if  that  table  of  corrections  were  applied 
to  observations  taken  in  any  year,  the  correction  would  not 
with  certainty  be  applied  advantageously,  though  of  course 
the  chances  are  that  they  would  be  so  applied. 

It  is  now  necessary  to  ascertain  if  this  variation  in  hypso- 
metrical  results  is  peculiar  to  the  climate  of  Switzerland,  or 
whether  it  is  applicable  to  other  countries.  The  observa- 
tions taken  in  the  Sierra  Nevada,  though  not  as  numerous 
as  are  desirable,  at  least  indicate  that  the  same  general  law 
holds  good  in  California;  but  while  observations  in  mid- 
winter give  the  least  results,  and  those  in  midsummer  the 
greatest,  the  range  is  twice  as  great,  which  may  be  attrib- 
uted to  the  higher  temperature  of  this  country.  The  mean 
temperatures  in  the  hottest  and  coldest  months  at  Geneva 
and  the  Grand  St.  Bernard  are  respectively  64°  and  31°  at 
the  former,  and  43^  and  15^  at  the  latter.  In  the  Sierra 
Nevada  we  have,  in  July,  at  Sacramento,  70-.0,  and  at  the 
summit,  about  7,000  feet  high,  5o°.o,  and  in  January  they 
are  48^.9  and  26^.3,  respectively. 

But  unfortunately  for  the  development  of  any  law  of 
practical  importance  that  can  be  of  use  in  making  a  table 
of  corrections  to  be  applied  to  results  obtained  in  different 
months  so  as  to  reduce  tliem  to  the  yearly  mean,  the  range 
in  the  variation  of  these  results  seems  to  depend  more  u[)on 
the  temperatures  of  the  stations  than  upon  the  difference  of 
altitude  between  them.  For  example,  the  range  between 
the  winter  and  summer  results,  as  develoi)ed  from  observa- 
tions taken  at  Sacramento  and  Fort  Churchill,  is  200  feet. 


45 

while  the  diiference  of  altitude  is  about  4,200  feet,  and  that 
from  observations  at  Sacramento  and  summit  of  the  Sierra 
Nevada  at  Hope  Valley,  about  7,000  feet,  is  118  feet.  This 
last  result,  however,  is  from  observations  in  the  single 
months  of  July  of  1860  and  January  of  1804. 

From  all  that  has  been  previously  pointed  out  on  this 
subject,  we  are  certain  that  hypsometrical  results  generally 
give  results  which  are  considered  greater  in  midsummer 
than  in  midwinter,  but  the  amplitude  of  this  variation  de- 
pends so  much  upon  the  climate  of  the  two  stations  that  no 
definite  rule  can  be  given  concerning  it. 

COiNCLUDlNG  REMARKS. 

In  the  previous  pages  I  have  explained  the  method  which 
I  have  recommended  to  be  adopted  in  i)roduciug  the  best 
hypsometrical  results,  the  essentic^l  points  of  which  are  to 
prepare  the  barometric  observations  beforehand  by  correct- 
ing them  for  the  horary  oscillation  of  the  barometer,  and 
then  to  use  the  mean  daily  temperature  during  the  period 
in  which  the  observations  were  taken,  whether  it  be  short 
or  long. 

Prof.  J.  I).  Whitney,  formerly  the  State  geologist  for  the 
State  of  California,  with  a  full  knowledge  of  my  method  as 
explained  in  Xo.  15  of  the  Professional  Pa[)ers  of  the  Corps 
of  Engineers,  has  adopted  another  method,  and  has  explained 
it  in  a  work  entitled  "Contributions  to  Barometric  Hypsom- 
etry,  with  tables  for  use  in  California."  In  the  first  chapter 
the  distinguished  professor  gives  an  able  and  learned  dis- 
cussion of  the  various  forms  of  the  barometric  formula 
which  have  been  used,  and  comes  to  the  conclusion  that  no 
change  in  any  of  the  constants  is  advisable.  He  says,  in 
the  beginning  of  his  third  chapter,  that  my  formula,  or  that 
of  Guyot  (which  is  almost  identical  with  it,  and  one  or  the 
other  of  which  was  used  by  him  and  his  assistants  during 
the  geological  survey  of  California),  "  is  the  one  which  leads 


46 

most  directly  to  practical  results,  and  upou  which  the  chief 
dependence  is  to  be  placed/' 

Tbe  third  and  last  chapter  of  this  work  is  also  interesting, 
but  the  second  one  is  the  onl^-  one  which  explains  his  method 
of  treating  barometric  and  thermometric  observations.  He 
had  obtained  observations  during  three  years  at  Sacra- 
mento, near  the  sea-level;  at  Colfax,  on  tbe  slope  of  the 
Sierra  Nevada,  at  an  altitude  of  2,414  feet;  and  at  Summit 
Station,  at  an  altitude  of  6,951  feet.  The  altitudes  were  as- 
certained during  the  leveling  for  the  railroad.  Tbe  obser- 
vations were  taken  at  7  a.  m.,  2  p.  m.,  and  9  p.  m.  From 
the  monthly  means  of  the  barometer  and  thermometer  at 
those  three  hours,  he  ascertains  how  much  the  mean  hypso- 
metrical  results  at  each  of  those  hours  in  each  month  at  each 
of  the  three  stations  differ  from  their  altitudes  as  given  by 
the  level.  He  then  forms  a  table  of  corrections  to  be  ap- 
plied to  such  results  from  observations  taken  in  tbe  field 
during  those  months  and  at  those  hours,  and  by  a  simple 
interpolation  assumes  corrections  for  the  intermediate  hours 
between  7  a.  m.  and  9  p.  m.  He  uses  the  actual  observa- 
tions of  the  barometer  and  thermometer  without  other  cor- 
rection than  that  of  reducing  the  barometer  to  32°  F.  From 
tbe  monthly  menu  i)ressure  and  temperature  at  each  of  the 
three  hours,  he  deduces  bis  table  of  corrections  to  be  ap- 
plied to  each  hour  of  the  day  and  month  of  the  year. 

My  method  is  to  eliminate  beforehand  all  causes  of  error, 
as  far  as  possible,  by  first  applying  a  correction  to  the  bar- 
ometric readings  so  as  to  get  rid  of  the  effects  of  the 
horary  oscillation,  and  then  to  eliminate  the  effects  of  the 
horary  movement  by  using,  instead  of  the  observed  tem- 
perature, the  mean  daily  air  temperature  for  tbe  period 
during  which  the  barometric  observations  were  taken. 

It  is  evident  to  me  that  Professor  Whitney's  method  must 
produce  more  "maximum  errors"  than  mine;  because  tbe 
periods  of  the  barometric  and  tbermometric  observations,  in 


47 

the  field  are  not  the  same  as  the  monthly  })eiiods  of  obser- 
vations nsed  by  him  in  preparing  his  table  of  corrections. 
Observations  in  the  field  are  usually  for  a  short  period ;  his 
table  of  corrections  is  from  the  monthly  means.  During  a 
barometric  reconnaissance,  the  altitudes  of  most  of  the  sta- 
tions on  the  line  are  approximately  determined  from  single 
observations.  In  forming  his  table  he  has  used  the  monthly 
mean  of  the  thermometer  at  the  three  observed  hours. 
Xow  it  is  well  known  that  during  a  month  the  range  of  the 
thermometer  during  the  twenty-four  hours  may  be  twice, 
three  times,  and  even  four  times  as  great  in  one  day  as  in 
auother.  If  observations  of  the  barometer  had  been  taken 
during  one  day  only,  it  might  have  happened  that  the  ther- 
uiometric  curve  (if  the  observations  had  been  plotted)  for 
that  day  was  a  maximum  or  a  minimuai,  and  the  horary 
thermometric  curve  from  the  actual  observatiotis  would  be 
quite  different  from  that  obtained  from  the  thermometric 
monthly-  mean.  With  regard  to  the  barometer,  its  horary 
oscillations  from  day  to  day  during  a  month  at  the  same 
place  are  so  nearly  alike  that  no  material  error  is  made  by 
adopting  either  the  horary  oscillation  for  the  month  or  that 
for  the  period  of  observation. 

Within  the  limits  of  the  State  of  California  almost  every 
variety  of  climate  is  to  be  found.  There  is  the  moist  and 
uniform  climate  of  the  coast,  and  the  arid  and  tropical  cli- 
mate of  the  Mohave  and  Coiorado  deserts.  There  are  vast 
plains  near  the  sea  level,  and  a  number  of  mountain  peaks 
between  fourteen  and  fifteen  thousand  feet  above  it.  When 
we  consider  the  greaL  change  of  temperature  during  twenty- 
four  hours  in  a  considerablj  portion  of  the  State,  the  great 
variation  in  the  range  of  that  temperature  in  different  days 
and  in  different  localities,  and  the  totally  different  character 
of  the  horary  oscillations  of  the  barometer  at  an  upper  and 
lower  station,  varying  as  these  do  with  altitude,  latitude,  and 
climate,  and,  more  than  all,  local  peculiarities  of  climate,  it 


48 


can  be  easily  umlerstood  that  it  is  impossible  to  adopt,  with 
good  results,  a  table  of  corrections  suitable  to  every  part  of 
such  a  State  as  California,  or  even  to  a  considerable  portion 
of  it. 

My  method  is  quite  as  easy  of  api)lication  as  that  of  Pro- 
fessor Whitney,  except  that  itre<iuires  a  certain  amount  of 
intelligence  in  the  computer,  who  has  to  i)repare  the  obser- 
vations and  apply  the  corrections  before  the  numbers  are 
used  in  computing  the  difference  of  altitude.  This  might  be 
considered  by  some  to  be  a  disadvantage,  for  with  bis 
method  any  ignorant  man,  possessed  of  a  small  amount  of 
knowledge  of  arithmetic,  can  become  a  baroujetric  compu- 
ter, by  following  certain  prescribed  rules.  But  I  take  it  for 
granted  that  all  persons  engaged  in  barometric  reconnais- 
sances of  any  importance  are  endowed  with  quite  enough 
intelligence  to  properly  prepare  barometric  and  therrao- 
metric  observat:ions  for  computation  by  my  method. 

It  is  of  the  utmost  importance  on  a  barometric  reconnais- 
sance that  we  should  know  as  nearly  as  possible  the  probable 
maximum  error,  because  the  results  are  only  to  be  fully 
trusted  up  to  that  limit.  The  method  which  produces  the 
least  maximum  error  must  then  be  considered  the  best.  I 
wish  now  to  show,  from  the  computed  results  of  observa- 
tions at  my  command,  that  the  method  adopted  by  Pro- 
fessor Whitney  does  actually  produce  more  maximum  error 
than  mine. 

For  that  purpose  I  have  used  ten  days'  observations  at 
Sacramento,  Placerville,  Strawberry  Valley,  and  Hope  Val- 
ley, in  August.  Observations  at  those  four  stations  are  the 
only  ones  at  my  command  which  are  suitable  for  the  i>urpose 
where  full  hourly  observations  were  taken.  I  calculated 
for  each  of  the  three  hours  during  the  ten  days  the  differ- 
ence of  altitude  by  the  two  methods.  1  then  made  fiom 
them  a  table  of  maximum  and  mean  errors,  which  is  here- 
with submitted. 


49 

It  will  be  seen  that  the  amount  of  error  in  hypsometrical 
results  is  over  forty  per  cent,  more  by  Professor  Whitney's 
method  than  by  mine,  and  any  intelligent  man  who  has 
carefully  studied  the  two  methods  can  easily  appreciate  the 
reason. 


Table  VIII. — Comparison  of  barometric  7'esuJt.s  by  Professor  Whttneifs  and 
Colonel  lilUiamson's  methods,  from  observations  taken  at  7  a.  m.,  2p.m., 
and  9  jj.  ni.,  during  ten  days  of  August,  1860. 

SACRAMENTO  AND  HOPE  VALLEY. 


Max.  error. 

Max.  error. 

Mean  error. 

Grand  mean. 

Whitney's  method 

Williaiusou's  method 

+  -249.  7 
+  155.7 

—  214.  5 

—  144.  2 

61.6 
54.5 

6,  976.  9 
6,  961.  7 

+       l.CO 

—      1.49 

1.13 

SACRAMENTO  AND  PLACERVILLE. 


+ 
+ 

37.9 

•21.9 

—  36.8 

—  24.6 

13.5 
13.0 

1,  f97.  0 

Williamson's  method 

1,918.4 

+ 

1.  36 

—       1. 50 

1.04 

PLACERVILLE  AND  STRAWBERRY  VALLEY. 


Whitney's  method    4-194.4 

Williamson's  method -|-  143.0 


+       1.36 


—  94.  1 

—  51. 5 


—       1.66 


42.1 
20.1 


3,  715.  0 
3,  731.  6 


STRAWBERRY  VALLEY  AND  HOPE  VALLEY. 


+     64.5 
+     49.2 

—  4.5.3 

—  41.0 

21.3 
21.0 

1,362.3 

Williamnon's  tuethod 

1,  368.  6 

Ratio ... 

+       L31 

—       1.10 

l.Ol 

4   U   B 


'ANPERiODTTr^ ^^'^^ 

<OME  USE  '^ 


'  ^^^  ^0.,  .'aT^^^^^^g^^^^ 


@s 


PAT.  JAN.  21.  \m 


- —                    

.?82800 

^ 

UNIVERSITY  OF  CALIFORNIA  LIBRARY 

U    C   BERKELEY  LIBRARIES 


CDt,l3b7^^=^ 


